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math.AP2019★ 1 cited
Anomalous dissipation, anomalous work, and energy balance for smooth solutions of the Navier-Stokes equations
Alexey Cheskidov, Xiaoyutao Luo
In this paper, we study the energy balance for a class of solutions of the Navier-Stokes equations with external forces in dimensions three and above. The solution and force are sm…
math.AP2019★ 3 cited
Normalized solutions for a fourth-order Schrödinger equation with positive second-order dispersion coefficient
Xiao Luo, Tao Yang
We are concerned with the existence and asymptotic properties of solutions to the following fourth-order Schrödinger equation \begin{equation}\label{1} Δ^{2}u+μΔu-λu={|u|}^{p-2}u,…
math.AP2019★ 13 cited
Stationary and discontinuous weak solutions of the Navier-Stokes equations
Alexey Cheskidov, Xiaoyutao Luo
We prove that there exists a nontrivial finite energy periodic stationary weak solution to the 3D Navier-Stokes equations (NSE). The construction relies on a convex integration sch…